U.S. patent number 5,834,925 [Application Number 08/853,156] was granted by the patent office on 1998-11-10 for current sharing power supplies with redundant operation.
This patent grant is currently assigned to Cisco Technology, Inc.. Invention is credited to Jay A. Chesavage.
United States Patent |
5,834,925 |
Chesavage |
November 10, 1998 |
Current sharing power supplies with redundant operation
Abstract
A plurality of power supplies are connected in parallel, each
power supply isolated from the others using a non-linear isolation
element such as a barrier diode. Feedback is furnished around the
non-linear isolation element such that the voltage drop of the
isolation element is reduced to be within the regulation range
desired. The non-linear characteristic of the isolation element
combined with feedback produces an output impedance which is low
for high currents, and exponentially higher for low output currents
for current sharing versus output offset voltage improvement.
Inventors: |
Chesavage; Jay A. (Palo Alto,
CA) |
Assignee: |
Cisco Technology, Inc. (San
Jose, CA)
|
Family
ID: |
25315226 |
Appl.
No.: |
08/853,156 |
Filed: |
May 8, 1997 |
Current U.S.
Class: |
323/272;
307/58 |
Current CPC
Class: |
H02J
1/108 (20130101) |
Current International
Class: |
H02J
1/10 (20060101); H02M 007/00 () |
Field of
Search: |
;363/65,69,70,71
;323/268,272 ;307/58,82,59 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Riley; Shawn
Attorney, Agent or Firm: Chesavage; Jay
Claims
I claim:
1. A redundant mode power supply comprising:
a power stage having an error signal as input and producing as
output a voltage proportional to said error signal;
a variable resistance element connected between said power stage
output and a power supply output, said variable resistance element
having a lower resistance for high currents passing through said
variable resistance element and a higher resistance for a minimum
current passing through said variable resistance element;
an error amplifier producing said error signal in proportion to a
gain constant multiplied by the difference between a reference
voltage and said power supply output voltage, said error amplifier
having a gain constant with a value of
where
A.sub.fzr is said error amplifier gain constant,
R.sub.d is a resistance of said variable resistance element
resistance at a maximum output current,
.vertline.Voa-Vout.vertline. is a absolute value of a difference
between said power stare output voltage and said power supply
output at said minimum load current,
I.sub.min is said minimum load current.
2. The power supply of claim 1 wherein said variable resistance
element is a semiconductor device.
3. The power supply of claim 2 wherein said semiconductor device is
a diode.
4. The power supply of claim 1 wherein said variable resistance
element is a material having a negative temperature
coefficient.
5. A plurality 2 to n of redundant mode power supplies connected in
a parallel configuration and having a common power supply output,
each power supply j comprising:
a power stage having an error signal as input and producing as
output a voltage proportional to said error signal;
a variable resistance element connected between said power stage
output and said power supply output, said variable resistance
element having a lower resistance for high currents passing through
said variable resistance element and a higher resistance for low
currents passing through said variable resistance element;
an error amplifier producing said error signal in proportion to a
gain constant multiplied by the difference between a reference
voltage and said power supply output voltage, said gain constant
having a value of
where
A.sub.fzr is said error amplifier gain constant,
R.sub.d is a resistance of said variable resistance element
resistance at a maximum output current,
.vertline.Vo(j)-Vo(mean).vertline. is an absolute value of a
difference between said power stage output voltage of said power
supply j and a power supply output voltage at said minimum load
current, and
I.sub.min is said minimum load current.
6. The power supply of claim 5 wherein said variable resistance
element is a semiconductor device.
7. The power supply of claim 6 wherein said semiconductor device is
a diode.
8. The power supply of claim 5 wherein said variable resistance
element is a material having a negative temperature
coefficient.
9. A redundant mode power supply having a single output voltage and
comprising:
a plurality n of power stages having an error signal as input and
producing as output a voltage proportional to said error signal,
each of said power stages having a gain P.sub.i where n is larger
than two, and i is an index having a value from 2 to n;
a plurality n of variable resistance elements connected between
each of said power stage output and said single output voltage,
said variable resistance elements having a lower resistance for
high currents passing through said variable resistance element and
a higher resistance for low currents passing through said variable
resistance element;
a plurality n of error amplifiers each having a reference voltage,
said error amplifiers producing n said error signals in proportion
to a gain constant K.sub.i multiplied by a difference between said
reference voltage and said power supply output voltages, each of
said error amplifiers individually providing said error signal to
each of said power stages;
said output stage gain constants P.sub.i and said error amplifier
gain constant K.sub.i are chosen such that
where
Zo.sub.i is an output impedance of each of n said power stages
operating at a minimum power stage output current added to a
resistance of each of i said variable resistance elements operating
at a minimum power stage output current,
.vertline.Vo.sub.i -Vout.vertline. is an absolute value of a
difference between said power stage n output voltage and said
output voltage at said minimum power stage output current, and
Imin is a minimum load current, equal to a sum of each of n said
minimum power stage output currents.
10. The power supply of claim 9 wherein said variable resistance
element is a semiconductor device.
11. The power supply of claim 10 wherein said semiconductor device
is a diode.
12. The power supply of claim 9 wherein said variable resistance
element is a material having a negative temperature coefficient.
Description
FIELD OF THE INVENTION
This invention is directed to the class of redundant mode power
supplies found in applications requiring very high reliability such
as networking equipment, wherein the loss of one or more power
supplies, or the mains power to one or more of such supplies should
not cause any disturbance in the operation of the equipment
receiving power.
BACKGROUND OF THE INVENTION
Redundant power supplies are used in networking equipment to
increase the overall reliability of the associated network
equipment. This improvement in reliability is available through
several mechanisms. The first mechanism of importance for increased
reliability during steady state, long term operation is lower
output current operating point, which results in lower operating
temperatures and currents within the power supply. The second
mechanism, which is important in the event of power supply
shutdown, mains power failure, or power supply failure is linear
operation, which is generally guaranteed by current sharing. As
long as all of the supplies present are current sharing, the
transient response of the power supply to this class of
disturbances is essentially governed by the same conditions which
afford well behaved load regulation characteristics. For example,
the load regulation of the power supply is typically very well
behaved, and for linearly operating power supplies, the failure of
one such supply appears to the remaining supplies as an incremental
step change in output current. By contrast, when power supplies are
not current sharing and the power supply delivering the bulk of the
current fails, the power supply that was formerly idling turns on
with non-linear characteristics similar to initial power-up,
causing the cessation of delivery of output power during this
turn-on interval, during which the equipment receiving power goes
through an interval of partial to complete loss of power.
The prior art in the area of redundant current sharing power
supplies falls into three general areas: droop sharing power
supplies, 3 wire control power supplies, and local sensing power
supplies. The first area pertains to droop sharing power supplies,
as in U.S. Pat. No. 4,924,170 (Henze) wherein the output impedance
of the supply is used to share load current. Disclosed in this
patent is local feedback of output current as a term which has the
overall effect of increasing the output impedance of the supply for
DC, while maintaining a low output impedance at higher
frequencies.
The second area is 3 wire control power supplies, wherein the
output of a high gain error amplifier is fed commonly to low gain
output stages to produce an common output, which requires sharing
of internal signals in addition to the usual combined outputs. One
example of this is U.S. Pat. No. 4,734,844 (Rhoads et al) which
describes a 3 wire regulation system wherein a master supply
generates a control output, and a plurality of slave units act on
this common control signal. This system has the weakness that if
one of the supplies contaminates the common control signal with
erroneous input, the entire system will replicate and produce an
erroneous output. Rhoads does not address redundancy in the sense
of immunity to component failure, but shows additional
interconnections between supplies for them to work properly. U.S.
Pat. No. 5,521,809 (Ashley et al) discloses a current sharing
circuit based on the power supplies exchanging information with
each other relating to the level of current sharing through a
separate bus wire, identified in the patent as a sharebus. Each
power supply has a local estimate of current being delivered, which
is compared with a fraction of the total current, and a local
feedback term is provided to each supply to achieve current
sharing. This method affords a high degree of accuracy in current
sharing, but does not address either on-line redundancy or
transient behavior. U.S. Pat. No. 5,122,726 (Elliott et al)
discloses overvoltage protection for redundant power supplies, and
discloses diode coupling as a means for achieving on-line isolation
between power supplies, and makes reference to the difficulty of
achieving current sharing or load regulation under this topology.
Also disclosed is current sharing in a master/slave relationship,
using a control signal common to all supplies. The inventive
elements of this patent are directed to an overvoltage circuit
which is able to monitor overall output voltage, and selectively
disable the defective power supply producing the overvoltage
condition.
A related method combining aspects of the first and third class of
sharing is shown in U.S. Pat. No. 4,618,779 (Wiscombe) which
describes a scheme for regulating a plurality of power supplies by
modulating the value of the sense resistor in the feedback loop via
an external controller which modulates this value based on sensing
current delivered by each supply to the load.
The third area is local sensing power supplies, in which a locally
sensed version of the output signal is compared with the total
output current, and the local error signal represents a combination
of output error signal and current sharing error. U.S. Pat. No.
4,035,715 (Wyman et al) describes a current sharing system wherein
the total system output current is made available to each supply so
as to ensure that each supply does not furnish more than its
proportion of total load current. U.S. Pat. No. 5,552,643 (Morgan
et al) describes a method of current summing wherein multiple
switch mode power supplies deliver current to a common inductor.
This addresses a method of current summing, but does not afford
redundant operation. U.S. Pat. No. 4,257,090 (Kroger et al)
describes a current sharing system wherein feedback is provided to
each power supply based on the sum of the output voltage and a
local measurement of inductor current, which ensures that each
power supply is operating below the maximum current as constrained
by a saturated output inductor. U.S. Pat. No. 5,477,132 (Canter et
al) is similar to Ashley, and discloses means for measuring a total
current, and delivering this measurement to the individual power
supplies, which compare this total value to their individual
contribution, and produce a local error term which is summed into
the regulation loop along with the global (output) voltage
regulation term. U.S. Pat. No. 4,866,295 (Leventis et al) describes
another technique for current sharing based on measurement of
output current from each supply being subtracted from a total
measured output, similar to that described by Canter and Ashley.
U.S. Pat. No. 4,766,364 (Biamonte et al) discloses a redundant
power supply having a common output filter and distributed diode
and inductor energy storage circuits. In this master/slave
configuration, the master power supply computes an error signal
that is distributed to the slave units. Each power supply further
has decision circuitry to take that unit off-line if there appears
to be a failure in that unit. A master error causes each slave
supply to furnish its own local error signal and ignore the master
signal.
SUMMARY OF THE INVENTION
The present invention allows power supplies to be connected in a
parallel configuration, wherein the combination of power supplies
share current without additional circuit complexity or overhead as
compared to individual supplies and therefore affords more reliable
operation. In general, the improvement in current sharing over
output voltage offset between power supplies with
parallel-connected outputs is roughly 10 times better than the
droop sharing configuration, and has no increased circuit
complexity when compared to competing schemes such as 3-wire
control, or local control, which require substantially more
components, many of which interfere with the premise of independent
operation of units implicit in the reliability calculations.
Therefore, a first object of the invention is a power supply which
shares current over a wide range of output currents. A second
object of the invention is a power supply which shares current
while maintaining a high tolerance to output voltage offsets and
drifts, particularly at low output currents. A third object of the
invention is a highly reliable current sharing power supply.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a prior art power supply having output summing
diodes.
FIG. 2 is a prior art system belonging to the class of current
sharing power supplies hereafter referred to as droop current
sharing power supplies.
FIG. 3 is a prior art system belonging to the class of current
sharing power supplies hereafter referred to as 3 wire control
current sharing power supplies.
FIG. 4 is a prior art system belonging to the class of current
sharing power supplies known as local current sensing current
sharing power supplies.
FIG. 5 shows the present invention incorporating the features of
diode current summing and output voltage feedback.
FIG. 6 shows the output and dynamic resistance characteristics of a
silicon schottky diode.
FIG. 7 shows the output characteristic of the power supply of FIG.
2 and FIG. 5.
FIG. 8 shows the current sharing characteristics of the power
supplies of FIGS. 2 and 5.
FIG. 9 shows a cross-regulating dual-output power supply.
SUMMARY OF THE INVENTION
Current sharing power supplies have the characteristic of sharing
output current over a range of output current. Redundant mode power
supplies have the characteristic of continuously providing output
voltage within tightly specified voltage limits throughout the life
of the equipment utilizing the provided power, including throughout
failure events in the power supplies. This disclosure is directed
at the class of power supplies responsible for both redundant and
current sharing operations. In modern networked computer systems,
for example, it has become critical to have both power supply
functions of redundancy and current sharing. There are several
topologies found for redundant mode power supplies. In one
topology, the primary mains power to each supply is furnished from
a different source to ensure continuous operation even if a mains
power source should fail. The default topology is the case where a
power supply furnishing some fraction of the load fails and goes
off-line. Regardless of topology, it is preferred to have a
plurality of power supplies operating with each supply sourcing a
fraction of the current such that the difference in current from
supply to supply is less than roughly 25% of the nominal current
obligation of that supply. While exactly dividing the current
between supplies may seem desirable, in practice negligible
incremental system benefit is derived. Much more significantly,
when a pair of power supplies are not current sharing, and the
power supply affording the majority of the current fails, the
idling power supply must instantaneously change from none to full
current. Generally, the transient output characteristic of a power
supply has two modes: The first mode is characterized by a fairly
fast transient response time associated with linear operation at
one operating point moving to a new linear point of operation. An
example of such linear operation is changing the load point from
10% or 50% of rated load to 100% of rated load. Such load point
adjustments can be made in a matter of milliseconds, or faster, and
are purely the consequence of the feedback control system
compensating the power supply. During this load point shift, the
power supply output voltage remains in regulation, and varies
typically less than 2% of nominal output voltage. The second mode
of dynamic operation is a supply moving from a point of idling, or
furnishing no output current to supplying full current. In this
case, the feedback loop is in a saturated off state, and must slew
the control signal to a full on condition, followed by regulation
to a stable operating point. Frequently, such supplies also have an
error output slew limiting circuit to prevent overvoltage at the
output of the supply during the power-up condition. The result is
that the saturation recovery time of the power supply is much
longer than the dynamic response time of the power supply. The
simplest way to ensure that the fastest response time, and
therefore the best dynamic regulation in the event of a power
supply failing, is to guarantee that the supplies current share
during proper operation. It should be clear to one skilled in the
art that the dynamic response time remains short even if the power
supply is operating at 10% of total load current. Since for
redundant operation, the power supply must be rated to carry the
full load if all the other supplies are turned off, current sharing
is generally not done for the purpose of reducing the stress level
seen by the supply during redundant operation, although the stress
level of the supply is nevertheless reduced by redundant operation,
and power supplies operated in this configuration generally operate
longer without failure than those operating at a higher load
point.
FIG. 1 shows a plurality of non-current sharing power supplies
connected together via summing diodes. In this configuration, each
of power supplies 10a-c (and associated sub-elements suffixed a-c
in the figures) comprise a pulse width modulator 11 driving an
output stage 19, which provides output voltage to isolation diode
13, which delivers power to load 18. Feedback resistors 14 and 15,
and stable reference source 16 provide an error input to the error
amplifier 12 such that the output voltage 17, shown as Vo is
stable. For a typical high gain operational amplifier 12, the
equation of operation would be:
and the DC operation of the entire circuit becomes:
where R.sub.14 and R.sub.15 are the values of elements 14 and 15
respectively,
V.sub.16 is the value of the stable reference source 16, and the
output delivered to the load 18 is Vo-V(D.sub.13) where V(D.sub.13)
is the voltage drop of diode element 13.
Diode 13 has intrinsic voltage drops as will be seen in FIG. 6
which make load regulation difficult. The variation in load current
will cause a variation in output voltage, creating what is
generally described as insufficient load regulation. Examining for
example moving between 1A point 82 and 10A point 83 of output
current, it can be seen that the diode voltage changes from 0.4 V
to 0.6 V, or 200 mV over this range. Because this voltage drop is
outside the feedback regulation loop, the entirety of this voltage
drop is seen by the load 18. It can be seen that although the diode
offers needed isolation between power supplies, it functions at the
expense of output load regulation.
General reliability of systems fall into two classes: series
systems and parallel systems. Given a series system comprising two
elements with failure rates respectively of .lambda.1 and .lambda.2
the respective reliabilities R.sub.1 and R.sub.2 may be may be
computed as
where R1 and R2 are the system reliabilities associated with
failure rates .lambda..sub.1 and .lambda..sub.2.
The total reliability rate for the series system RT=R1*R2.
MTBF, or Mean Time Before Failure, is defined as 1/.lambda.
For the case where the failure rate for a power supply is known to
be .lambda..sub.1 =10/10.sup.6 hours, the reliability over 10.sup.6
hours is
Rsupply=exp (-10)=4.54.times.10.sup.-5, while for the diode the
failure rate .lambda.2=0.1/10.sup.6 hours and the related
reliability over 10.sup.6 hours is
Rdiode=exp (-0.1)=0.905
In the case where two such components are placed in series, the
reliability decreases to
Rdiode+supply=(4.54.times.10.sup.-5) (0.905)=4.11.times.10-.sup.5,
corresponding to a failure rate of 10.1 every 10.sup.6 hours, and
we can see that the incremental decrease in reliability (from 10 to
10.1 in 10.sup.6) by adding a comparatively reliable diode is
small. The related MTBF values are as follows:
For 2-unit redundant systems the MTBF is found to be 3/2.lambda.,
while for 3-way redundant systems, the MTBF is found to be
11/6.lambda.. For repairable systems reporting power supply failure
status, it is rarely necessary to use more than 3 power supplies in
such a configuration.
If we were to use two such diode+supply combinations and put them
in parallel, we would find
MTBF(2.times.diode+supply)=(3/2)99,010=148,515 hours. This
improvement increases dramatically when system reporting of power
supply failures is taken into account, and the failed power supply
is replaced before a final power supply failure occurs.
FIG. 2 shows a droop sharing configuration. Power supplies 30 have
outputs connected together via droop sharing resistance 33. The
other elements error amplifier 32, pulse width modulator 31,
feedback resistors 34 and 35, and voltage reference 36 maintain the
same functions as described earlier. The purpose of this droop
sharing resistance 33 is to balance the current sharing between
power supplies. The value of 33 is typically set to cause less than
0.5% output regulation drop. For example, in a 5 V, 10 A power
supply, the droop resistance 33 would be 0.005.OMEGA., which would
produce a 50 mV output drop at full load. The droop sharing
configuration is an improvement over the diode sharing
configuration of FIG. 1, in terms of improved output voltage
regulation (in this example, 50 mv versus 200 mv of FIG. 1)
however, a new operating constraint is present. In order for each
power supply to be guaranteed of delivering current to the load,
rather than idling, the offset between power supplies must be
or, conversely the minimum load related to achievable offsets would
be
Vo.sub.a and Vo.sub.b are each the respective differences between
output voltage from each supply. For example, if one power supply
furnished 5.005 v and the other furnished 4.995 v,
.vertline.Vo.sub.a -Vo.sub.b .vertline.=0.010 v.
Rd is the droop resistance of each power supply=0.005.OMEGA.for our
example
Imin is the minimum load current drawn under operating
conditions
For the case where .vertline.Vo1-Vo2.vertline.=10 mV, a typical
value for modern supplies, and Rd=0.005.OMEGA., the minimum current
would be 1 A, which means that for a load of 1 A, one of the
supplies would be furnishing all of the output current, and the
other would be marginally operating. Load currents above 1 A would
share for the excess of the current above 1 A, so for example a 2 A
load would cause one supply to deliver 0.5 A, and the other to
deliver 1.5 A. The alternative to achieving lower minimum load
current would be to increase Rd to a larger value at the expense of
load regulation, or use power supplies with tighter voltage
offsets, trade-offs which have traditionally caused difficulties in
droop sharing power supplies. The principal advantage of droop
sharing power supplies is simplicity, as each supply is operating
separately and summing its output.
FIG. 3 discloses the 3 wire method of current sharing. In this
scheme, previously described elements voltage reference 42, high
gain amplifier 43, pulse width regulator 44, and voltage divider 40
and 41 operate as shown in FIG. 1. High gain amplifier 43 is of the
transconductance type operating into a load resistor 46, such that
the modified equation of operation for elements 43 and 46 are
the expression (10.sup.6 /R46) is the transconductance gain, and is
scaled by R46 in this example to produce the same gain as was
produced earlier in FIG. 1, such that adding more amplifiers and
gain setting resistors 46 does not modify the gain of the resultant
circuit. The purpose of choosing a transconductance type amplifier
is to enable a summed output connection, wherein the various error
amplifier signals are summed together to produce a common error
signal 48. This error signal is then fed to the low-gain pulse
width amplifiers 44 and output stage 47, which due to low gain
would tend to current share to within 20% of nominal current. While
this represents a great advantage in terms of current sharing over
droop sharing, it has problematic reliability elements. For
example, the control signal 48 is shared over all supplies, and
should some sort of failure occur in this signal, no isolation
would occur, and this disturbance would propagate through all
supplies, and to the load 49. As can be seen, the failure tolerance
of this configuration is compromised, and attempts to address this
simply add more elements and complexity.
FIG. 4 is the prior art scheme referred to now as local current
sensing. Again, previously described elements error amplifier 50,
voltage divider 53 and 52, reference voltage source 51 maintain
their previously described functions. New elements local current
sense amplifier 55, local current summing resistor 56, total
current amplifier 59, and total current summing resistor 57.
Typically, resistors 56 and 57 provide balancing currents to node
58 such that when the amplifier is providing a proper share of
total current, these currents balance, and when the amplifier is
providing less or more than the expected current, an additional
error signal is provided to encourage respectively greater or
lesser output voltage to compensate. As can be seen, many new
elements have appeared, and while the interests of current sharing
may be served, those of reliable redundancy are not. Single points
of failure can be identified, such as the total current sensor 59,
and in the event of total loss of a single power supply, while the
remaining power supplies will current share, the output voltage
will statically drop, as the current sharing balance of node 43
will indicate that each power supply is sourcing more than its
expected contribution of output current.
FIG. 5 shows the new configuration for a scalable, current sharing
redundant mode power supply operating over a wide range of total
load currents. Previously disclosed elements voltage reference 70,
error amplifier 71, voltage divider 72 and 73, pulse width
modulator 74, and summing diode 75 are operating in the new
topology wherein the feedback point is taken after the summing
diode. In prior art power supplies, and as shown previously, the
gain of element 71 is chosen to be quite high, a result which
produces very good output load and line regulation.
Consequentially, this selection of high feedback loop gain also
produces a very low output impedance, such that the resultant power
supply could be used in the droop sharing circuit of FIG. 1 with
the addition of a droop sharing resistor 31 outside the feedback
loop as shown in FIG. 2. As will be seen, the characteristics of
the error amplifier 71 will be chosen such that summing diode 75
produces a low output resistance at high current for good load
voltage regulation, and the diode characteristic combined with
feedback will produce a desired higher output impedance at lower
currents for improved current sharing over a very wide range of
load currents.
FIG. 6 shows a diode characteristic curve 84 for output current
versus voltage for a typical schottky barrier diode, such as
Motorola device MBR1035. While curve 84 is an actual diode curve,
the general form of this curve is of the well known formula
I=I.sub.o e.sup.(V/Vt), where
Io is the leakage current of the diode, often measured in the
reverse bias condition,
V is the applied diode voltage
Vt is 0.026 V at room temperature, as derived from the familiar
formula Vt=kT/q, where k is Boltzmann's constant, T is the
temperature in Kelvin, and q is the electron charge constant.
The dynamic resistance of this curve is numerically evaluated for
various currents and is shown logarithmically as curve 85, which
can be seen to vary from 10 m.OMEGA. to 300 m.OMEGA. at diode
currents of 10 A to 1 A respectively. As can be seen, the diode
resistance curve 85 shows a drop in resistance with increased
applied current. This is desired for achieving good load regulation
at high currents in our power supply 76, however, if this diode is
used in the circuit of FIG. 1 at currents varying from 1 to 10
amperes, the output voltage drop in moving from point 83 to point
82 would be an intolerable 250 mV.
If we solve the equations of operation for the circuit of FIG. 5,
we develop the following relationships:
R.sub.72, R.sub.73, R.sub.74 are the resistance of the named
elements 72 through 74,
Z.sub.75 is the combined resistance of the PWM output stage and
summing diode 75,
A.sub.71 is the gain of the error amplifier
K.sub.74 is the gain of the pwm output stage
Vo, Vm, Io are the voltages and currents shown in FIG. 5, and
solving these for the dynamic output resistance
.increment.Vo/.increment.Io, we determin e
for simplicity, we will use
A.sub.fzr ={1+(K.sub.74 A.sub.71 R.sub.72)/(R.sub.72 +R.sub.73)} to
denote feedback impedance reduction.
The physical interpretation of this output resistance from FIG. 5
shows that the output resistance Z.sub.75 is reduced by the loop
gain {1+(K.sub.74 A.sub.71 R.sub.72)/(R.sub.72 +R.sub.73)}.
Ordinarily, the objective of such an exercise would be to drive the
loop gain to a very high value to ensure high voltage stability. We
will instead select a gain based on the characteristic of summing
diode 75 to produce a desired level of current sharing. Returning
again to FIG. 6, we can see that the dynamic resistance of the
diode, as shown as a function of output current by curve 84, varies
from 10 m.OMEGA. to 300 m.OMEGA. at diode currents of 10 A to 1 A.
From the formula above for Zo, it is now possible to choose gain
elements which allow the selection of the output impedance of the
power supply at a particular operating current. Furthermore, if
this impedance is chosen at the maximum output current to satisfy
the desired current sharing level, the same scaling factor present
in equation for A.sub.fzr will scale the curve 83 of FIG. 6 to
produce better current sharing tolerance of output offset between
supplies at lower operating currents. For example, if we use the
earlier computed values:
then the value from FIG. 6 would be 30 m.OMEGA..
We would then select values for the feedback reduction factor would
be
0.001=0.030/A.sub.fzr, and we would compute A.sub.fzr =30.
It should be clear to one skilled in the art that while a diode
characteristic is shown for a device with impedance decreasing with
increasing current, many such other semiconductor and resistive
devices having such a characteristic are available, including
fast-acting resistors having a negative resistance temperature
coefficient, although the diode is believed to be superior because
it is part of the circuit affording redundancy and load isolation.
It is also clear that many values of A.sub.fzr could be used which
advantageously provides an output resistance profile scaled to
particular system requirements.
FIG. 7 shows the output droop characteristics, where curve 90 shows
the output characteristics for the standard droop supply of FIG. 2
with the above values, and curve 91 represents the characteristic
of FIG. 5 for the case where the overall diode drop is scaled to be
the same as the droop resistance.
FIG. 8 shows the current sharing results for the power supply with
this characteristic. Curve 92 shows the current sharing versus
offset voltage between supplies for the droop configuration of FIG.
1, while curve 93 shows the improved current sharing achieved with
the diode-feedback configuration of FIG. 5. As is clear from FIG.
8, the diode circuit of FIG. 5 results in an order of magnitude
improvement in current sharing, with negligible degradation in load
regulation.
As should be clear to one skilled in the art, the basic elements of
a PWM, error amplifier, power output stage, voltage reference, and
voltage divider could be modified individually or collectively to
achieve scaling of the diode characteristic to produce the desired
non-linear output resistance characteristic so as to encourage
current sharing at low currents between supplies, but the best mode
for such an arrangement is shown for illustrative purposes. As an
example of such a rearrangement, FIG. 9 shows a cross regulated
power supply wherein the reduction in gain is the result of
feedback of two different output voltages. In this case, the gain
of the error amplifier could be taken to be very high, and the gain
reduction comes about from the cross regulation of the two output
voltages. Inclusion of the summing diode in this feedback circuit
has the same effect as the earlier illustration wherein the error
amplifier was shown with limited gain. Examining in detail the
operation of the parallel power supplies 100, there is shown
reference voltage 104, error amplifier 105, pulse width modulator
106, and dual output stages 107 and 108, each having gains
respectively of K2 and K1, and load resistors 111 and 110. Solving
the equations for a single power supply circuit 100a or 100b
operating into load resistors 110 and 111, we can derive the
following:
where V.sub.ref is the reference voltage of source 104, Rp is the
parallel resistance of elements 101, 102, and 103, R.sub.101,
R.sub.102 and R.sub.103 are the resistances respectively of
elements 101, 102, and 103, K1 and K2 are the gain constants of
output sections 108 and 107 respectively, Av is the gain of error
amplifier 105, R.sub.109 is the dynamic resistance of diode 109.
From the equation for output resistance, we can evaluate for equal
values of R101, R102, and R103 and a very large value for Av, as is
typical for error amplifiers operating at maximum DC gain, and
derive the following expression for output resistance: V1/I1=Z1
=R.sub.109 {K.sub.2 /{K.sub.1 +K.sub.2 }}. As can be seen from this
expression, the diode resistance R109 is scaled by {K.sub.2
/{K.sub.1 +K.sub.2 }}, while Av was allowed to become very large.
As should be clear to one skilled in the art, many different forms
of diode scaling are available to accomplish current sharing
through increased dynamic resistance at low currents compared to
higher currents, as illustrated in this example. The operation of
parallel supplies 100a and 100b is identical to the operation
outlined in FIGS. 6, 7, and 8 with regard to current sharing
characteristics.
* * * * *